A BE35 PLT; DEPARTING VGT; TOOK OFF ON THE WRONG RWY; HAVING A POSSIBLE GND CONFLICT IN DOING SO.

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PERFORMED PREFLT; STARTED ENG; AND CALLED GND CTLR FOR TAXI CLRNC STATING LOCATION ON FIELD; WITH CURRENT ATIS; AND 'UNFAMILIAR WITH AREA AND WOULD APPRECIATE ANY ASSISTANCE.' GAVE DEST; DIRECTION OF FLT (NE); AND REQUESTED RADAR SVCS. INFORMED TO TAXI TO RWY 12R; THEN GND CTL ISSUED PROGRESSIVE TAXI INSTRUCTIONS; AND RECOMMENDED DEP HEADING 340 DEGS. 'XPONDER CODE SHORTLY.' TAXIED TO R AND STOPPED TO PERFORM RUN-UP AND DEPART RWY 12R FROM THAT POS. GND CTLR STATED; 'RUN-UP AREA TO RWY 7 TO YOUR L.' THERE WERE 2 CESSNA'S PERFORMING RUN-UPS AT TXWY F; AND I GOT INTO POS BEHIND THEM AND PERFORMED MY RUN-UP. MY L MAGNETO HAD SOME ROUGHNESS; AND THE CESSNAS DEPARTED DURING THIS TIME. TAXIED UP TO THE HOLD LINE AT TXWY F; CHANGED TO TWR FREQ AND ANNOUNCED I WAS '#1; READY FOR DEP; STILL DID NOT HAVE A SQUAWK.' TWR GAVE ME THE XPONDER CODE AND CLRED ME FOR TKOF. DIALED IN XPONDER CODE AND TAXIED FROM TXWY F ONTO THE DEP END OF RWY 7. I QUICKLY ADVANCED THE THROTTLE (DID NOT WANT TO BE SITTING ON AN ACTIVE RWY AT A BUSY ARPT) WHILE CHKING ON ENG PERFORMANCE DUE TO THE MAGNETO ROUGHNESS AT RUN-UP. I WAS ALMOST TO THE INTXN OF RWYS 12R AND 7 WHEN I REALIZED I WAS ON RWY 7 AND NOT RWY 12R AND WAS MENTALLY QUESTIONING MY RUN-UP CLRNC. THERE WERE NO AIRPLANES DIRECTLY IN FRONT OF ME ON RWY 7 AND A CESSNA WAS TURNING FINAL FOR ONE OF THE PARALLEL 12 RWYS. I COULD NOT EASILY SEE OVER MY SHOULDER TO CHK FOR TFC ON RWY 12R AND SINCE TRYING TO STOP WOULD PLACE ME ON 1 AND POSSIBLY 2 ACTIVE RWYS WITH LNDG TFC; I PROCEEDED WITH A TKOF ROLL ON RWY 7 AS THE SAFEST OPTION. THE TWR CTLR STATED I HAD DEPARTED THE WRONG RWY ON CLBOUT. CONTRIBUTING FACTORS AND HUMAN PERFORMANCE CONSIDERATIONS: 1) GND CTLR'S INSTRUCTIONS OF RUN-UP AREA OF RWY 7 TO MY L. 2) PLT UNFAMILIAR WITH ARPT. 3) THE 2 ACFT IN RUN-UP AREA GAVE THE PERCEPTION OF THE CORRECT RWY. 4) USE OF MULTIPLE RWYS PLACED INCREASED DEMANDS OF SITUATIONAL AWARENESS ON PLTS AND CTLRS. 5) ENG ROUGHNESS AND XPONDER CODE GIVEN RIGHT AT DEP WERE DISTRACTIONS. 6) HIGH PERCEIVED ARPT TFC VOLUME BY TRANSIENT PLT. 7) PLT FATIGUE WAS A SIGNIFICANT CONTRIBUTING FACTOR AFFECTING JUDGEMENT AND SITUATIONAL AWARENESS. SHOULD HAVE QUERIED THE GND CTLR ABOUT A RWY CHANGE AFTER THE CTLR COMMENTS ABOUT RWY 7.